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Math Help - 4-regular Graph

  1. #1
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    4-regular Graph

    Prove there is precisely one 4 regular graph on 6 vertices.
    any advice will help
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  2. #2
    Junior Member guildmage's Avatar
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    I don't know if this will work but have you tried showing that any two 4-regular graph on 6 vertices are isomorphic?
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  3. #3
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    Quote Originally Posted by guildmage View Post
    I don't know if this will work but have you tried showing that any two 4-regular graph on 6 vertices are isomorphic?
    well i tried to get 4,4,4,4,4,4 down to C4 and show that its unique subgraph and build my way up
    i not sure if that will work either...but i m not so good with isomorphic
    i usually make a mistake going there
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  4. #4
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    4 regular graph on 6 vertices.

    Quote Originally Posted by AwesomeDesiKid View Post
    Prove there is precisely one 4 regular graph on 6 vertices.
    any advice will help
    That will be a graph obtained by removing 3 edges from complete graph on 5 vertices .

    proof .
    consider 5-regular graph with 6 vertices it is nothing but complete graph on 5 vertices .Now you need to reduce one degree for each of six vertices that is you need to remove 3 edges.
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  5. #5
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    4-regular graph with 6 vertices

    That will be a graph obtained by removing 3 edges from complete graph on 5 vertices .

    proof .
    consider 5-regular graph with 6 vertices it is nothing but complete graph on 5 vertices .Now you need to reduce one degree for each of six vertices that is you need to remove 3 edges.
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